Coaxially printed magnetic mechanical electrical hybrid structures with actuation and sensing functionalities

Soft electromagnetic devices have great potential in soft robotics and biomedical applications. However, existing soft-magneto-electrical devices would have limited hybrid functions and suffer from damaging stress concentrations, delamination or material leakage. Here, we report a hybrid magnetic-mechanical-electrical (MME) core-sheath fiber to overcome these challenges. Assisted by the coaxial printing method, the MME fiber can be printed into complex 2D/3D MME structures with integrated magnetoactive and conductive properties, further enabling hybrid functions including programmable magnetization, somatosensory, and magnetic actuation along with simultaneous wireless energy transfer. To demonstrate the great potential of MME devices, precise and minimally invasive electro-ablation was performed with a flexible MME catheter with magnetic control, hybrid actuation-sensing was performed by a durable somatosensory MME gripper, and hybrid wireless energy transmission and magnetic actuation were demonstrated by an untethered soft MME robot. Our work thus provides a material design strategy for soft electromagnetic devices with unexplored hybrid functions.

angles for different core-sheath fibers. Unlike the high-modulus copper wire that constrains the deformation, the liquid metal core with high fluidity does not evidently impair the magnetically induced deformation. The MME fiber thus has similar flexibility as its hollow counterpart (filled with air). The remanence increases with the increase of NdFeB content; a high content of NdFeB particles can help enhance the magnetically actuated deformability of the MME fiber/structure. However, with the increase of NdFeB contents, yield stress of the composite ink also increases, making it hard to print the composite ink; also a high NdFeB content also reduces the flexibility of the MME fiber/structure. As shown in Supplementary Fig. 4c and d, as the NdFeB content increases, elastic modulus of printed MME fibers increases and the tensile strength decreases. After systematic investigation, the composite ink was optimized to have a NdFeB particle content of 50 wt% (the mass ratio of PDMS to NdFeB particles is 1:1). Supplementary Figure 5. Schematic diagram of the magnetization process. In step Ⅰ, the cured unmagnetized MME structure was placed in a mold with a predesigned geometry. In step Ⅱ, the unmagnetized MME structure was elastically deformed by the mold and placed in a pulsed magnetic field Bmag (about 3 T). Under the action of a pulsed magnetic field Bmag, the MME structure would reache its saturation magnetization, with the magnetization direction same as the pulsed magnetic field Bmag. In step Ⅲ

Supplementary
, after the MME structure is released from the mold and re-coiled to its initial deformation free geometry, a magnetization profile m would be imparted onto the MME structure. In this process, magnetization profile m of the MME structure can be controlled by designing the geometry of the mold and adjusting the pulsed magnetic field Bmag.
Supplementary Figure 6. Schematic diagram of the magnetically actuated deformation of a magnetized MME structure. Interaction between the external actuation magnetic field Bact and the magnetization profile m will generate a spatially varying magnetic torque Tm, across the MME structure. Tm would deform the MME structure till an equilibrium state is achieved. The direction of the magnetization profile m tends to coincide with the direction of the actuation magnetic field Bact. As h increases, overlapping between adjacent layers decreases, affecting the structure fidelity; meanwhile, a smaller h would affect MME structures' conductivity. At h = 800 μm, the 3D MME structure with high structure fidelity and electrical conductivity can be fabricated. and the magnetic field module for the finite element models of the MME fiber and MME coil structure.

Supplementary
(f-g) Boundary condition settings for the solid mechanics module and the magnetic field module in the finite element model of the magnetically actuated deformation process of the MME fiber and MME coil structure.
The magnetization and magnetic actuation deformation of MME structures were analyzed by COMSOL Multiphysics 6.0 (COMSOL Inc., Sweden). The multi-physics models of FEA were built in a 500×500×500 mm 3 cube space, which mainly consisted of air, coil (180 mm in diameter), and MME structure. The tetrahedral grid was used to divide the model, and the grid size ranged from 0.16 mm to 2.2 mm, as shown in Supplementary Fig. 25a-b. The FEA of magnetization includes two analysis steps: the calculation of the structure bending process under external volume force using the solid mechanics module in stationary and the analysis of the MME structure magnetization profile under 3 T pulsed magnetic field using the magnetic field module in time dependent. The boundary condition settings for the solid mechanics module and the magnetic field module for the finite element models of the MME fiber and MME coil structure as shown in Supplementary Fig. 25d. The length of the fixed surface is 9 mm, and the volume force is applied to deform the MME fiber and MME coil structure. The folded MME structure was magnetized using a pulse current to the coil, which could generate a 3 T pulse magnetic field in the magnetism module, as shown in Supplementary Fig. 25e. The pulsed magnetic field is shown in Supplementary Fig. 25c.
After calculating the magnetization profile m in the MME structure, the magnetic actuation deformation was analyzed by coupling the magnetic field-no current module with the solid mechanics module ( Supplementary Fig. 25f). The magnetic actuation deformation of each step was analyzed by interactive calculation of magnetic force using the magnetic field-no current module and the deformation using the solid mechanics module. The magnetic force on the MME structure was calculated by integrating the magnetic stress tensor induced by the interaction between actuation magnetic field Bact and the calculated magnetization profile m. The boundary condition settings of the MME fiber and MME coil structure as shown in Supplementary Fig. 25g. Finally, the final magnetic actuation deformation of the MME structure could be obtained by iterative calculation in multi-steps.
Supplementary Figure 26. Measurement of the magnetic flux density B at 1 mm from the MME fiber with a gauss meter.
Supplementary Figure 27. The L-shaped mold for magnetizing a MME fiber.
Supplementary Figure 28. Quasi-static analysis of the MME fiber. The bending moment acting on an infinitesimal section of a MME fiber under equilibrium-state deformation is shown in the inset. Therefore, On the basis of the theoretical framework developed for ferromagnetic soft materials 30 , we provide the fundamental equations for quantitative description of the deformation of MME structure upon magnetic actuation. The vector m represents the magnetization of the infinitesimal section of the MME fiber in the initial undeformed state.
The magnetic moment Mnet is expressed as: Where A is the cross-sectional area.
Along the neutral axis of the MME structure, it can be segmented into infinitesimal coaxial elements.
where E1 and E2 are Young's moduli of the sheath and the liquid metal core, respectively. I1 and I2 are the moments of inertia of the sheath and the liquid metal core, respectively.
The curvature k(s) at position s can be calculated as: where θ(s) is the rotation angle at position s, which can describe the target shape of the MME structure programmed under the continuous magnetization profile m, the total rotation angle θ(s) at x is expressed as: